\(\Omega (\pi )\)  is group-sparse regularizer, and it expects that each target sample receives masses only from source samples that have the same label. And following [1]}, we define the regularizer as \(\Omega (\pi ) = \sum _j \sum _{cl} ||\pi (I_{cl}, j)||_2\) , where \(||\cdot ||_2\)  denotes the \(l_2\)  norm and \(I_{cl}\)  contains the indices of rows in \(\pi \)  related to source domain samples of class \(cl\) . \(\pi (I_{cl}, j)\)  is a vector containing coefficients of the \(j\) th column of \(\pi \)  associated to class \(cl\) , and it induces the desired sparse representation in the target samples. \(\lambda \)  and \(\eta \)  are hyper-parameters.
We use generalized conditional gradient (GCG) following [1]} to solve the optimization problem.
